Department of Mathematical Sciences



Further Differential and Integral Calculus

The Calculus of this module is a continuation of that of Engineering Mathematics 115. The following topics are covered:  Hyperbolic functions; L’Hospital’s rule; more integration techniques;  simple differential equations (separable and first order linear); parametric equations; polar coordinates and polar graphs; conic sections; quadratic surfaces and functions in two variables; complex numbers; matrix algebra.

Module Information

  • 38571 145 (15) Engineering Mathematics 145
  • Year 1, semester 2 of the Programmes in all engineering disciplines.
  • Lecturing load: 5 lectures, 1 tutorial of 2 hours per week.
  • Prerequisite: Engineering Mathematics 115.
  • Language specification : A & E


  • Ms L Wessels: Office 1009BD, Industrial Psychology/Mathematics Building  (e-mail:
  • Dr C Naude:  Office 1023A, Industrial Psychology/Mathematics Building (e-mail:
  • Prof M Wild: Office 1023D, Industrial Psychology/Mathematics Building  (email:
  • Dr D Ralaivaosaona: Office 3004, Industrial Psychology/Mathematics Building (e-mail:

Study Material

Prescribed textbooks:

  • James Stewart, Calculus (7th Edition). Chapters 6,7,9,10,12,14 are covered.
  • Dennis G Zill/Warren S Wright, Advanced Engineering Mathematics (4th Edition). Chapters 8 and 17 (selected topics).
  • Class notes on Weierstrass substitution and rationalising substitution.

Learning Opportunities

  • The learning material is fully covered during the lectures.
  • During the tutorial periods students have the opportunity to solve problems under supervision and to obtain assistance with regard to aspects that may be unclear.
  • Solutions to class problems or interesting and/or more difficult problems appear from time to time on SunLearn.


  • The assessment follows the general rules of the Faculty of Engineering. The final mark for this course consists of the following:
    • Semester Mark (SM): Average mark of the tutorial tests that are written every Thursday.
    • Assessment opportunity A1
    • Assessment opportunity A2
  • The mark is calculated as follows: Final mark (FM) = 0.2 x SM + 0.3 x A1 + 0.5 x A2
  • A third assessment opportunity A3 is offered for students who miss opportunity A1 or A2 because of illness or some other valid reason, and for students with a final mark between 40 and 50.
  • Students have to obtain at least 40 in either A2 or A3 to pass.

General Information

  • Please note the following arrangements with regard to tutorials: (a) Attendance of all tutorials is compulsory, also for students who are repeating the course. (b) Students who are repeating the course and who have tutorial clashes with another (second-year) tutorial or practical class, must make arrangements to write the tutorial tests during the tutorial sessions.
  • Pocket calculators may not be used in tests and examinations.

Study Tips

  • It is important that you understand the basic theory well so that it can be applied. You should therefore first study the definitions and theorems thoroughly.
  • In order to determine whether you have mastered the work, you should regularly do a variety of problems from the Exercises in the textbook. The lecturer may highlight a number of these problems during the lectures, but they remain your own responsibility and will not be marked.
  • Feel free to ask your lecturer for assistance if you do not understand something or are stumped by a problem. The lecturer is available immediately after the end of each class, as well as in his/her office (preferably by appointment).
  • Revise each paragraph fully after it has been dealt with in class. Make sure that you do not fall behind, as it is very hard to catch up later.


A student who has passed this module should possess the following skills:

  • Is able to continue with ease with the Engineering Mathematics prescribed in the second year for the programmes concerned.
  • Is able to recognise and apply indefinite integration techniques.
  • Understands and can apply other aspects of Calculus, as set out in the module contents above.
  • Understands complex numbers and complex functions.
  • Is able to do matrix algebra and solve systems of linear equations.